The beam-hardening effect is one of the most important factors of metal artifact that degrades CT image quality. In the polychromatic X-ray, this occurs noticeably when scanning metallic materials with large changes in energy-dependent attenuation coefficient. This violates the assumption of a CT reconstruction based on a fixed attenuation coefficient in a monochromatic X-ray, which leads to beam-hardening artifacts such as streaking and cupping shapes. Numerous studies have been researched to reduce the beam-hardening artifacts. Most of the methods need the optimization based on iterative reconstruction, which causes a time-consuming problem. This study aims at an efficient methodology in terms of performance time while providing acceptable correction of beam-hardening artifacts. For this, the attenuation coefficient error due to beam hardening is modeled with respect to the length of the X-ray passing through the metallic material. And the model is approximated by a linear combination of four basis functions determined by the length. The linearity is also preserved in the reconstruction image, so that the coefficient of each basis function can be obtained by solving the minimization problem of the variance of the homogeneous metal region in the image. For the evaluation, a phantom including three titanium rods was scanned by a cone-beam CT system (Ray, South Korea) and the images were reconstructed by the standard FDK algorithm. The results showed that the proposed method is superior in terms of speed while delivering acceptable beam-hardening correction compared to recent methods. The proposed model will be effective for the applications where processing speed is important for the beam-hardening correction.